||Ralph Abraham, Gerrold E. Marsden, Tudor Ratiu, Richard Cushman
||Addison-Wesley Publishing Company
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Since the time when the very first release of this book appeared fifty years ago, a truly great deal of activity has been there in simplistic geometry and also in the Hamiltonian systems. The general audience of the present edition of the volume remains the same as it used to be for the initial one, namely practicing engineers working in the field of mechanics and interested in the geometrical methods, physists, mathematicians and other professionals. The authors have also included the fundamental results in manifold theory plus the most important facts from the point set topology. Significant updates have been made relating to the qualitative theory and symmetry groups, several completely new chapters addressing the rigid body, mechanics, topology and quantization, plus other chapters; many corrections have been made to the original content of the volume. The book is divided into four major parts - the first part is titled Preliminaries and covers the differential equations and calculus of manifolds, while the second part deals with the analytical dynamics covering the Langrangian and Hamiltonian systems, mathematical systems etc. The third part of the book provides an outline of the qualitative dynamics, including topological, differentiable and Hamiltonian dynamics. The last part is dedicated to the celestial mechanics...